Damped oscillations in a multiple delayed feedback NF-κB signaling module

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

No gene has garnered more interest than p53 since its discovery over 40 years ago. In the last two decades, thanks to seminal work from Uri Alon and Ghalit Lahav, p53 has defined a truly synergistic topic in the field of mathematical biology, with a rich body of research connecting mathematic endeavour with experimental design and data. In this review we survey and distill the extensive literature of mathematical models of p53. Specifically, we focus on models which seek to reproduce the oscillatory dynamics of p53 in response to DNA damage. We review the standard modelling approaches used in the field categorising them into three types: time delay models, spatial models and coupled negative-positive feedback models, providing sample model equations and simulation results which show clear oscillatory dynamics. We discuss the interplay between mathematics and biology and show how one informs the other; the deep connections between the two disciplines has helped to develop our understanding of this complex gene and paint a picture of its dynamical response. Although yet more is to be elucidated, we offer the current state-of-the-art understanding of p53 response to DNA damage.

Approximating the energy landscape of a two-dimensional bistable gene autoregulation model by separating slow and fast dynamics

The energy landscape is widely used to quantify the stability of multistable nonlinear systems, such as bistable gene regulation networks. In physics, the potential can be obtained through integration only for gradient systems. However, multidimensional nonlinear systems are often nongradient, for which the potential is calculated by decomposing the dynamics to gradient and nongradient parts. This potential is then called a quasipotential. Given that one-dimensional (1D) systems can be regarded as gradient systems, we attempt to separate the two-dimensional (2D) system into two 1D systems working on distinct timescales, and the potential can be easily calculated for the two 1D systems separately. This method is used in this study to estimate the energy landscape of a two-variable gene autoregulation model. This elegant and comprehensive method is accessible for 2D nonlinear systems in which the dynamics can be divided into slow and fast parts.